The standard SI WIMP-nucleus interaction in the galactic standard halo
scenario [1]}, [2]}, [3]} is the benchmark that is used to
compare different experiments. The physical interpretation of the observed results
changes under different hypotheses for the interaction.
Such a consideration is important given the present unclear experimental
landscape. On the one hand,
DAMA [4]}, [5]}
recorded a signal that is interpreted as collisions of WIMPs with mass of
a few tens of \(\mathrm {GeV/c^2}\)  and the CDMS II-Si [6]}
result appears to be better fitted by a model with WIMPs than by one
with only reasonable backgrounds. On the other hand, the lack of signals
in other experiments, such as Xenon100 [7]}, LUX [8]}, PANDAX-II [9]}, and XENON1T [10]}
seems to contradict the existence of WIMPs of this mass, if the SI interaction is coherent and
independent of the nucleus
[11]}.
WIMP-nucleus interactions that differ from the
lowest-order SI one could alleviate the tension between experiments that use different target
nuclei. In fact, cross sections from other operators can depend on characteristics
of the target nuclei besides the mass number \(A\) . In particular, they can uniquely
depend on the WIMP mass and velocity yielding interaction rates that span many
orders of magnitude [12]}, [13]}, [14]}, [15]}, [16]}, [17]}.
